A294986 Number of compositions (ordered partitions) of 1 into exactly 7n+1 powers of 1/(n+1).

1, 41245, 4561368175, 1104353764428365, 396695587555058190126, 174436242482643190451211853, 86237678200608256132213084584295, 46050764886573707269872023694736134925, 25997337847684377365651388718120083246723460

Offset: 0

Author

Alois P. Heinz, Nov 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..170

Crossrefs

Row n=7 of A294746.

Programs

Maple

b:= proc(n, r, p, k) option remember;
      `if`(n (k-> `if`(n=0, 1, b(k*n+1, 1, 0, n+1)))(7):
seq(a(n), n=0..12);

Mathematica

b[n_, r_, p_, k_] := b[n, r, p, k] = If[n < r, 0, If[r == 0, If[n == 0, p!, 0], Sum[b[n - j, k*(r - j), p + j, k]/j!, {j, 0, Min[n, r]}]]];
a[n_] := If[n == 0, 1, b[#*n + 1, 1, 0, n + 1]]&[7];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Formula

a(n) ~ 7^(7*n + 3/2) / (8 * Pi^3 * n^3). - Vaclav Kotesovec, Sep 20 2019